Closed Loop Controller and Method for Fast Scanning Probe Microscopy

ABSTRACT

A method of operating a metrology instrument includes generating relative motion between a probe and a sample at a scan frequency using an actuator. The method also includes detecting motion of the actuator using a position sensor that exhibits noise in the detected motion, and controlling the position of the actuator using a feedback loop and a feed forward algorithm. In this embodiment, the controlling step attenuates noise in the actuator position compared to noise exhibited by the position sensor in a bandwidth of about seven times the scan frequency. Scan frequencies up to a third of the first scanner resonance frequency or greater than 300 Hz are possible.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.11/800,679, filed May 7, 2007 and issued as U.S. Pat. No. 8,904,560,entitled Closed Loop Controller and Method for Fast Scanning ProbeMicroscopy. The subject matter of this application is herebyincorporated by reference in its entirety.

STATEMENT OF GOVERNMENT INTEREST

This invention was made with United States government support awarded bythe following agency: NIST/ATP (Award #70NANB4H3055). The United Stateshas certain rights in this invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The preferred embodiments are directed to a controller for a scanningprobe microscope (SPM), and more particularly, a controller for an SPMthat enables improved scanning speeds while maintaining the ability toobtain high quality sample data.

2. Description of Related Art

A scanning probe microscope, such as an atomic force microscope (AFM)operates by providing relative scanning movement between a measuringprobe and a sample while measuring one or more properties of the sample.A typical AFM system is shown schematically in FIG. 1. An AFM 10employing a probe device 12 including a probe 14 having a cantilever 15.Scanner 24 generates relative motion between the probe 14 and sample 22while the probe-sample interaction is measured. In this way images orother measurements of the sample can be obtained. Scanner 24 istypically comprised of one or more actuators that usually generatemotion in three orthogonal directions (XYZ). Often, scanner 24 is asingle integrated unit that includes one or more actuators to moveeither the sample or the probe in all three axes, for example, apiezoelectric tube actuator. Alternatively, the scanner may be anassembly of multiple separate actuators. Some AFMs separate the scannerinto multiple components, for example an XY scanner that moves thesample and a separate Z-actuator that moves the probe.

In a common configuration, probe 14 is often coupled to an oscillatingactuator or drive 16 that is used to drive probe 14 at or near aresonant frequency of cantilever 15. Alternative arrangements measurethe deflection, torsion, or other motion of cantilever 15. Probe 14 isoften a microfabricated cantilever with an integrated tip 17.

Commonly, an electronic signal is applied from an AC signal source 18under control of an SPM controller 20 to cause actuator 16 (oralternatively scanner 24) to drive the probe 14 to oscillate. Theprobe-sample interaction is typically controlled via feedback bycontroller 20. Notably, the actuator 16 may be coupled to the scanner 24and probe 14 but may be formed integrally with the cantilever 15 ofprobe 14 as part of a self-actuated cantilever/probe.

Often a selected probe 14 is oscillated and brought into contact withsample 22 as sample characteristics are monitored by detecting changesin one or more characteristics of the oscillation of probe 14, asdescribed above. In this regard, a deflection detection apparatus 25 istypically employed to direct a beam towards the backside of probe 14,the beam then being reflected towards a detector 26, such as a fourquadrant photodetector. Note that the sensing light source of apparatus25 is typically a laser, often a visible or infrared laser diode. Thesensing light beam can also be generated by other light sources, forexample a He—Ne or other laser source, a superluminescent diode (SLD),an LED, an optical fiber, or any other light source that can be focusedto a small spot. As the beam translates across detector 26, appropriatesignals are transmitted to controller 20, which processes the signals todetermine changes in the oscillation of probe 14. In general, controller20 generates control signals to maintain a relative constant interactionbetween the tip and sample (or deflection of the lever 15), typically tomaintain a setpoint characteristic of the oscillation of probe 14. Forexample, controller 20 is often used to maintain the oscillationamplitude at a setpoint value, A_(S), to insure a generally constantforce between the tip and sample. Alternatively, a setpoint phase orfrequency may be used.

A workstation is also provided, in the controller 20 and/or in aseparate controller or system of connected or stand-alone controllers,that receives the collected data from the controller and manipulates thedata obtained during scanning to perform point selection, curve fitting,and distance determining operations. The workstation can store theresulting information in memory, use it for additional calculations,and/or display it on a suitable monitor, and/or transmit it to anothercomputer or device by wire or wirelessly. The memory may comprise anycomputer readable data storage medium, examples including but notlimited to a computer RAM, hard disk, network storage, a flash drive, ora CD ROM. Notably, scanner 24 often comprises a piezoelectric stack(often referred to herein as a “piezo stack”) or piezoelectric tube thatis used to generate relative motion between the measuring probe and thesample surface. A piezo stack is a device that moves in one or moredirections based on voltages applied to electrodes disposed on thestack. Piezo stacks are often used in combination with mechanicalflexures that serve to guide, constrain, and/or amplify the motion ofthe piezo stacks. Additionally, flexures are used to increase thestiffness of actuator in one or more axis, as described in copendingapplication Ser. No. 11/687,304, filed Mar. 16, 2007, entitled“Fast-Scanning SPM Scanner and Method of Operating Same.” Actuators maybe coupled to the probe, the sample, or both. Most typically, anactuator assembly is provided in the form of an XY-actuator that drivesthe probe or sample in a horizontal, or XY-plane and a Z-actuator thatmoves the probe or sample in a vertical or Z-direction.

As the utility of SPM continues to develop, a need has arisen forimaging different types of samples at greater speeds to improve samplemeasurement throughput (e.g., more than 20 samples per hour) and/ormeasure nanoscale processes with higher time resolution than currentlyavailable. Although AFM imaging provides high spatial resolution(nanoscale), it has generally low temporal resolution. Typical highquality AFM images take several minutes to acquire, especially for scansizes above a few microns.

Several factors can limit imaging speed, including the cantileverresponse time, the usable scanner bandwidth in X, Y and Z directions,the power and bandwidth of the high voltage amplifier that drives thescanner, the speed of the cantilever force sensing, as well as thedemodulation system and the tracking force feedback system.

SPM images are typically constructed of arrays of measurements recordedat different locations on the sample. For example, an image may containthe local value of the relative sample height measured over an array ofdifferent XY locations on the sample. Alternative measurements caninclude amplitude, phase, frequency of the cantilever, electric andmagnetic forces, friction, stiffness of the sample, etc.

In this regard, relative positioning between the probe and sample isvery important. The quality of the acquired data, and resultantimage(s), depends on the system knowing the precise location where datais collected. It follows that position errors cause image degradation, aproblem exacerbated by operating the AFM at greater bandwidths.

A significant challenge in this regard is that piezoelectric stacks,tubes and other types of SPM actuators are imperfect. When consideringdesired scanning motion, the ideal behavior would be actuator movementsubstantially linearly in proportion to the voltage or other controlsignal applied. Instead, actuators, including piezo stacks, often movein a non-uniform manner, meaning that their sensitivity (e.g.,nanometers of motion vs. applied voltage) can vary as the voltageincreases. Moreover, drift, hysteresis and creep of the actuator operateto further compromise precisely positioning the probe and/or sample.With respect to hysteresis, for example, the response to an incrementalvoltage change will depend on the history of previous voltages appliedto the actuator. Hysteresis can therefore cause a large prior motion tocompromise the response to a commanded move, even many minutes later.After the command voltage is applied, the piezo may move a desireddistance, but continues to move uncontrollably due to the creep effect.Such effect can be more than 10% of the commanded motion, causing asubstantial positioning error.

Notably, these issues exist whether the probe device of the AFM iscoupled to the actuator (i.e., the case in which the probe device movesin three orthogonal directions), or the sample is coupled to theactuator. Moreover, though known solutions attempt to overcome theabove-noted challenges, they have been imperfect.

For example, some open loop methods of driving the SPM actuator havebeen implemented in an attempt to compensate for limitations of thecontroller and actuators, and thereby limit poor tracking betweendesired scanning movement and actual movement. The actuators may becalibrated, for example, by applying a voltage, for example, to the X-Yactuators and then measuring the actual distance that the sample orprobe travels. A look-up table may then be created, and then, inoperation, the actuator position can be estimated by monitoring thevoltage that is applied to the X-Y and/or Z actuators. In another openloop alternative, the scanner and its motion can be modeled usingrigorous mathematical techniques.

More specifically in this regard, turning to FIG. 2, open loop solutionstypically involve providing a unique drive signal u_(o) 41 that isapplied to an actuator or scanner 42 of an AFM 40 to provide scanningmotion between the AFM probe and the sample. The drive signal isderived, for example, from a model or a look-up table and corresponds tothe desired motion of the actuator. The drive signal u_(o) is intendedto produce actual scanner motion that substantially tracks the desiredmotion to produce uniform scanning. See for example U.S. Pat. No.5,557,156, owned by Veeco Instruments Inc., which describes applyingnon-linear drive voltages having a shape defined by a set ofpre-calibrated data, to piezo actuators to drive them into substantiallylinear motion. The set of data may also be called a scan table. Thistechnique has been successful for counteracting actuatornon-linearities, but the calibration procedure is cumbersome and it doesnot adequately address drift and creep. Additionally, the actuatorresponse depends strongly on scan speed requiring increasingly complexcalibration and lookup tables as SPM scan speed increases. When thescanner turns around for scanning the next line or offsets to adifferent position, a transient response can be excited. Such transientscan compromise data integrity. For example, transients 43 shown in FIG.2 can exist at the turn points of a typical raster scan drive 41.Notably, to minimize transients at turning points, an alternative drivemay be employed. As shown in FIG. 3, an AFM 44 may employ a drive 45that is rounded at the turn points. This solution operates well to quiettransients at a relatively low scan rate, but at the higher scan ratethe scanner motion (as shown by curve 46) still does not follow thedesired trajectory (raster scan corresponding to the triangle wave form47) in most cases. Moreover, due to the rounding, the usable range ofthe drive is limited.

Because such open loop solutions can be complicated and often still donot provide acceptable position accuracy, especially at higher scanspeeds, some SPMs employ closed loop position control. Such systemsimprove accuracy by using an auxiliary position sensor in a feedbackarrangement to actively monitor actuator movement, i.e., to determinehow well the actual movement is tracking the commanded movement, anddynamically adjusting the control signal applied to the appropriate SPMactuator(s). In this way, the actuator can be driven in a linear way tofollow a predetermined trajectory, compensating for non-linearity,hysteresis, and drift simultaneously. As a result, more accurate imagescan be obtained. However, the bandwidth of the position control feedbackis often limited (discussed below), and the noise introduced by thesensor employed to detect actual scanner motion can degrade imagequality through the feedback loop, thus further limiting the ability ofthe AFM to track a fast command signal during scanning, and thus produceacceptable images, at greater speeds. Due to the noise limitation, manyposition control feedback systems are disabled at small scan sizes. Insum, at higher imaging speeds, the performance of the position feedbacksystem often degrades SPM system performance.

Returning to the details of closed loop position control, we turn toFIG. 4. A closed loop control system 50 is used to drive the actuator tofollow a desired trajectory while minimizing position errors. Areference waveform 51 is generated as model for the desired scannermotion, a triangle wave in the example. Position sensor 54 measures theactual movement of scanner 52 and transmits that sensed signal to asumming block 56 (e.g., a digital sum or analog summing circuitry) thatgenerates an error signal representing the difference between thedesired motion of the scanner and actual scanner movement. Severalauxiliary displacement or position sensors have been proposed and/orused for monitoring actuator movement, including Linear VariableDisplacement Transducers (LVDTs), capacitance sensors, strain gauge andinductance sensors, and optical sensors including, for example, opticaldisplacement sensors (ODSs) and optical interferometers. Any alternativesensor that provides a predictable and calibratable output as a functionof relative position may be used. These sensors typically operate aspart of a closed loop controller associated with the scanner to correctfor differences between desired and actual movement.

A controller 58, such as a proportion and integral (PI) controller (or,for example, a double integrator) generates a control signal, u_(c), inresponse to the error signal which is used to drive the scanner.Controllers have been implemented with both all analog electronics anddigital feedback loops run by digital signal processors (DSP), fieldprogrammable gate arrays (FPGA) and other embedded controller anddigital computing devices, including personal computers. The controlsignal operates to compensate for measured position error produced bythe scanner, for example, caused by creep and drift.

Although useful for minimizing the effects of system conditions thathave an adverse impact on the ability of the scanner to track desiredmotion, the bandwidth of conventional control systems 50 is limited.There are several reasons for the limits in conventional positioncontrol systems, including scanner resonances and position sensor noiseand bandwidth limitations.

First, the resonant properties of the scanner must be considered. Eachturnaround in the triangle wave reference waveform 51 creates asubstantial impulse force on the scanner that can excite unwantedparasitic resonances. These resonances can also couple between axes andshow up in the measured motion of the cantilever's relative motionvis-à-vis the sample. Conventional AFMs either scan slow enough toreduce the amplitude of unwanted oscillation to an acceptable leveland/or trade off some scan range to round the tops and bottoms of thetriangle wave reference, as noted previously in connection with the openloop system shown in FIG. 3. The inability of SPM scanners to scan largeareas at high speeds without unwanted oscillations is a major bottleneckto operating SPMs at greater speeds.

Additionally, these resonances limit how fast the controller 58 canoperate. A feedback loop will go unstable if there is a gain of morethan one with a phase shift of 180 degrees. A simple mechanicalresonance of the scanner will accumulate 90 degrees of phase shift and asubstantial gain amplification at the resonance peak. The gain (andhence bandwidth) of controller 58 is limited to compensate for the phaseshift and gain of the scanner's mechanical resonance(s). Even before thecondition of instability, underdamped resonances can cause oscillationsand overshoot in the actual motion of the scanner. As a result,operation of conventional position control feedback loops is limited toa small fraction of the scanner's lowest observed resonance, or“fundamental resonant frequency.” Notably, the lowest observed resonanceis most often axis dependent, with coupling of the response typicallybeing present among axes, thereby limiting the lowest observed resonanceof the scanner/actuator.

Moreover, sensor 54 introduces noise to the system that compromises thecontroller's ability to satisfactorily track the desired motion. Theimpact of sensor noise is shown schematically in FIG. 4. (In practice,of course, the sensor noise accompanies the signal) Both the scanner'sreal position and the sensor noise (signal 55) are compared to thereference and the resultant error processed by controller 58. Thecontroller thus attempts to have the scanner respond to both the realposition error and the unwanted sensor noise, thus producing actuatormotion illustrated by signal 53. The resulting image is thereforecorrespondingly compromised by all the sensor noise that is within thefeedback bandwidth. The control signal u_(c), though compensating forsystem dynamics including thermal drift and creep, may not yield thedesired scanner motion because of the additional high frequency noiseintroduced via the sensing scheme. Sensor noise is typically a functionof bandwidth, so the position sensor electronics and/or the controllermay limit the bandwidth of the sampled position sensor signal to reducethe image of this noise. The effect of a limited sensor bandwidth,however, is typically the accumulation of phase shifts in the sensoroutput versus the actual motion of the scanner. These phase shifts thenlimit the maximum gain and bandwidth that can be employed by thecontroller 58. The practical effect of sensor noise and bandwidth inthis case is that the speed of scanning must be correspondingly reducedto maintain an acceptable level of position noise for acquiring highquality data.

Several groups have also developed schemes to counteract the effects ofunwanted resonances of the scanner by developing model based controlschemes. Authors on this subject include Stemmer, Schitter, Ando,Salapaka, and Zou, for example. In a typical model-based controller forSPM, the dynamic properties of the scanner are measured and an optimalclosed-loop control scheme is designed to maintain stability of thefeedback loop over a wide bandwidth. A typical first step is systemidentification, a procedure that maps the amplitude and phase responseof the scanner versus frequency, defining characteristics known as the“transfer function.” This transfer function may be used in a controllerthat achieves the highest scanner bandwidth, while also attempting tominimize oscillations due to unwanted resonances. Typical closed loopcontrol strategies in this regard include H-infinity or H2 controllersthat are described in the literature. Alternative schemes includeintentionally adding impulse transients to the control waveform timed tocounteract the impulse at the triangle wave turn-around. For example, animpulse force can be applied to the scanner at a time corresponding tohalf the oscillation period of the fundamental resonance. Destructiveinterference will occur between the results of the two impulses andquickly damp the unwanted oscillation. That said, because such closedloop schemes are intended to operate over a wide bandwidth, the problemsassociated with sensor noise continue to limit system performance.

An open loop model based controller, while compensating for scannerresonances, will still be subject to unwanted motion within the system,including scanner nonlinearities, creep and thermal drift. Thus,tracking in such systems remains imperfect. To accommodate degradedimage quality, open loop feed forward controllers have been developedthat attempt to model system factors, such as nonlinearities, creep andthermal drift, that impact the resultant data to produce an optimizeddrive waveform. Such models associated with feed forward controllers aredifficult to control and typically produce less than ideal results,primarily due to the challenge of creating a workable model that fitsall desired imaging conditions. Such imaging conditions often produce achange in the mechanical environment and therefore a change of thetransfer function used in the model. Ultimately, producing linearscanner motion is very difficult to achieve with these open loopsolutions. Therefore, an improvement was desired.

In the end, most often the design of the AFM must navigate a tradeoffbetween low noise performance (e.g., open loop) and image positioningaccuracy (e.g., closed loop). According to one type of open loop AFMscan controller, the control scheme utilizes a calibrated scanner andcorresponding input signal, such as a modified triangle wave, that isconfigured to account for system irregularities (e.g., resonances) whenscanning. Such open loop systems utilizing a feed forward model minimizeadverse effects on positioning due to system noise because extraneousstructure (such as an auxiliary sensor) is minimized. However, accurateoperation of the scanner and ultimate image accuracy is controlled bythe system's ability to accurately characterize the scanner andotherwise account for environmental effects such as drift and creep.This is most often a difficult task that typically yields an imperfectresult, given the inability to accurately model or predict particularenvironmental conditions. Moreover, due to this difficulty, such systemsare not sufficiently robust for many applications. The open loop feedforward scheme can be effective in compensating the scannernon-linearity if the calibration is accurate and remains constantthroughout the usage, but it still does not address the resonancedistortion introduced by the impulse forces at the turning point of thelinear triangular scanning.

The field of scanning probe microscopy was thus in need of a controllerthat facilitates tracking fast scanner movement with low noise whilealso compensating for position skewing operational conditions such asthermal drift and creep. Ideally, a closed loop scanner that minimizesthe impact of sensor noise on system performance was desired.

SUMMARY OF THE INVENTION

The present invention overcomes the drawbacks of prior art AFMs usingeither open loop or closed loop position controllers by using anadaptive feed forward algorithm in conjunction with a closed loopfeedback controller that attenuates high frequency noise introduced tothe control scheme by the feedback sensor. The feedback loop operates atlow bandwidth (less than the scan frequency) but is sufficient tocompensate low frequency position errors introduced by phenomena such asthermal drift and creep. The feed forward algorithm is employediteratively to achieve a threshold error (e.g., peak error of about 1%of initial scan range) in a minimum amount of time. Scan speedssignificantly greater than that supported by current AFM scancontrollers (from a few Hertz to, with the present invention, tens ofHertz, and even several hundred Hertz) can be achieved withoutcompromising image quality.

According to a first aspect of one embodiment, a method of operating ametrology instrument includes generating relative motion between a probeand a sample at a scan frequency using an actuator. The method includesdetecting motion of the actuator using a position sensor that introducesnoise in the actuator motion, and controlling the position of theactuator using a feedback loop and a feed forward algorithm. The feedforward portion of the control performs high bandwidth position trackingby adaptively, e.g., iteratively, optimizing the feed forward waveform.The adaptive optimization can be performed, for example, upon the changeof scan size, scan angle and speed. In one embodiment the sensorresponses are averaged through multiple cycles of motion (data smoothingmay also be employed) to substantially reduce the influence of thesensor noise. Once the feed forward algorithm achieves a minimum orthreshold scan error, the finalized feed forward waveform (e.g., scantable) is used to drive the scanner in an open loop manner, yet stillpreserves the linearity of the sensor as if it were running in a closedloop manner. Such operation allows high speed scanning over various scansizes, including very small scan sizes without the adverse impact ofsensor noise.

More specifically, the feed forward algorithm includes using aninversion-based control algorithm that uses a transfer functionassociated with the actuator. The scanner drive derived from theinversion-based control algorithm predicts the impact dynamics at theturn around of the repetitive scanning and compensates the impactthrough a modified drive so that the physical motion of the scannerfollows the trajectory of the reference substantially precisely. In afurther aspect of this embodiment, the inversion-based control algorithmiteratively produces a correction that contributes to a control signalthat compensates for non-linearities of the actuator.

According to yet another aspect of this embodiment, the control signalproduces a peak position error of less than about 1% of the total scanrange after no more than about 10 iterations of 10 scan lines periteration. More preferably, the control signal produces a peak positionerror of less than about 1% of the total scan range after no more thanabout 5 iterations.

In a still further aspect of this embodiment, the scan frequency is atleast 1/100^(th), and preferably, 1/10^(th) the fundamental resonantfrequency of the actuator. More preferably, the scan frequency is atleast ⅓^(rd) the fundamental resonant frequency of the actuator.

According to another aspect of this embodiment, the resonant frequencyof the actuator is greater than about 900 Hz and the scan frequency isat least about 10 Hz, but preferably the scan frequency is at leastabout 100 Hz. More preferably, the scan frequency is at least about 300Hz.

According to a still further aspect of this embodiment, a method ofoperating a metrology instrument includes generating, with an actuator,relative motion between a probe and a sample at a scan frequency over aselected scan size, from tens of nanometers to tens of microns, anddetecting motion of the actuator using a position sensor. The methodalso includes controlling, with at least one of a feedback loop and afeed forward algorithm, the generating step to substantially follow areference signal to achieve an integral position error of the relativemotion compared to the reference signal that is less than about 1% ofthe scan size. In this case, the contribution of the position sensornoise is reduced to less than about 1 Angstrom RMS, by averaging thedata during iterations. In the one embodiment, the scan bandwidth isequal to about at least seven times the scan frequency.

In another aspect of this embodiment, the bandwidth of the feedback loopis much less than the scan frequency, sufficient substantially only tocorrect very slow drift due to piezo creep.

In yet another aspect of this embodiment, a scanning probe microscope(SPM) includes an actuator that generates relative motion between aprobe and a sample at a scan frequency. The SPM also includes a positionsensor that detects motion of the actuator and generates high frequencynoise, while a controller generates a position control signal based onthe detected motion. In this embodiment, the controller attenuates thenoise to less than about 1 Angstrom RMS within a noise bandwidth equalto at least seven times the scan frequency.

In another aspect of this embodiment, the feed forward algorithmincludes using an inversion-based control algorithm that is usediteratively to produce a correction of the scanning drive wave form thatcontributes to a control signal that compensates for non-linearities ofthe actuator. In one embodiment, the correction is a scan table.

According to a still further aspect of this embodiment, a method ofoperating a metrology instrument includes generating relative motionbetween a probe and a sample at a scan frequency using an actuator. Themethod also includes detecting motion of the actuator using a positionsensor, the position sensor exhibiting noise in the detected motion. Themethod also compensates for position error of the actuator using both afeedback loop and a feed forward algorithm in which the bandwidth of thefeedback loop is less than the scan frequency.

In yet another embodiment, a method of operating a metrology instrumentincludes generating relative motion between a probe and a sample at ascan frequency using an actuator. The method further includes detectingmotion of the actuator using a position sensor which exhibits noise inthe detected motion. The position of the actuator is controlled using afeedback loop and an adaptive feed forward algorithm. More particularly,the controlling step attenuates impact of the noise in the detectedmotion on the actuator motion over a noise bandwidth equal to at leastseven times the scan frequency. And, the adaptive feed forward algorithmrepeatedly updates the generating step in response to the detectedmotion of the actuator.

According to another aspect of this embodiment, the adaptive feedforward algorithm iteratively determines a correction to the generatingstep. Notably, the generating step includes using a reference signalthat is a triangle wave, and the method may include reducing ripple inthe triangle wave using a window. In one example, a Hanning window isused.

These and other features and advantages of the invention will becomeapparent to those skilled in the art from the following detaileddescription and the accompanying drawings. It should be understood,however, that the detailed description and specific examples, whileindicating preferred embodiments of the present invention, are given byway of illustration and not of limitation. Many changes andmodifications may be made within the scope of the present inventionwithout departing from the spirit thereof, and the invention includesall such modifications.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred exemplary embodiments of the invention are illustrated in theaccompanying drawings in which like reference numerals represent likeparts throughout, and in which:

FIG. 1 is a block diagram illustrating a prior art scanning probemicroscope (SPM), appropriately labeled “Prior Art”;

FIG. 2 is a block diagram illustrating a prior art open loop SPMscanner, appropriately labeled “Prior Art”;

FIG. 3 is a block diagram illustrating an alternate prior art open loopSPM scanner, appropriately labeled “Prior Art”;

FIG. 4 is a block diagram of a prior art closed loop SPM scanner,appropriately labeled “Prior Art”;

FIG. 5 is block diagram of a controller according to a preferredembodiment that utilizes low gain feedback and a high bandwidth feedforward algorithm to provide uniform scanner motion, schematicallyillustrating sensor noise essentially eliminated from the actuatormotion;

FIG. 6 is a block diagram of a closed loop scanner having a parallelfeed forward control loop according to a preferred embodiment;

FIG. 7 is a flow chart illustrating operation of the adaptive feedforward algorithm of the controller of FIG. 6;

FIG. 8 is a block diagram illustrating production of an initial scantable for the feed forward algorithm;

FIGS. 9A and 9B are graphs illustrating the transfer function of theactuator, including the amplitude and the phase responses, respectively;

FIG. 10 is a graph illustrating the performance of the controller shownin FIG. 6, particularly in reducing positioning error;

FIG. 11 is a graph illustrating a blown-up version of the graph in FIG.10;

FIG. 12 is a graph illustrating operation of the feed forward algorithmof FIG. 7, with and without calibration;

FIG. 13 is a graph illustrating position sensor noise power densityversus operating frequency, illustrating a scan bandwidth selected fordesired noise attenuation;

FIGS. 14A, 14B and 14C illustrate sample images taken by an AFMemploying a controller according to the preferred embodiments; and

FIGS. 15A, 15B and 15C schematically illustrate images of a samplehaving a sharp edge, using the preferred embodiments.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The preferred embodiments of the present invention are directed to aclosed loop SPM scanner having a low bandwidth feedback control loopcombined with a parallel feed forward control loop that improves AFMscan speed while maintaining positioning integrity so that imagedegradation typically seen at higher scan speeds is minimized. Morespecifically, the feed forward algorithm uses an inversion-basedalgorithm to intelligently control the drive signal applied to thescanner at high bandwidth so that actual scanning motion tracks thedesired scanner motion. And, by operating the feedback control loop withrelatively low gain, the adverse positioning effects due to highfrequency noise (e.g., sensor noise), are substantially minimized.Overall, open loop SPM performance (i.e., low noise) is achieved withminimal image degradation.

To highlight the benefits of the preferred embodiments, reference isinitially made to FIGS. 4 and 5. In FIG. 4, as a standard controller 58for a typical AFM includes a high gain feedback loop that measures andmonitors the movement of a scan actuator in comparison to a referencesignal to attempt to maintain uniform motion in an intended path (e.g.,a raster scan). Though operating to provide relatively uniform andlinear actuator motion, the sensor used in the feedback loop introducesa noise component “n” to the detected motion 55 that is processed bycontroller 58. As a result, actuator motion, though substantially linearis compromised by the noise introduced by the sensor signal 92. Thecorresponding data, therefore, may, and typically does, yield a degradedimage, especially at small scan sizes. Furthermore, the limited feedbackbandwidth causes an increased tracking error at higher scan rate,yielding a distorted image at higher scan rate. Turning to FIG. 5schematically illustrating the apparatus of the preferred embodiments, acontroller 90 similarly acquires a sensor signal that includes sensornoise, “n,” but the controller includes an architecture that has a feedforward component that operates in conjunction with a feedback componentoperating at low gain (i.e., low bandwidth, e.g., less than the scanfrequency) to minimize the impact of sensor noise on the control signalapplied to the scan actuator, and thus actuator motion 94 moreaccurately follows the desired reference signal 96. With the highfrequency portion of the sensor signal 92 (i.e., noise) attenuated,image degradation is significantly lessened. Overall, whereas prior artAFMs with closed loop scanners may include sensor noise in the range ofup to about 2 nm RMS, controller 90 attenuates sensor noise so it can bemaintained at less than about 0.1 nm RMS during scanning. As a result,much greater scanning speeds can be achieved without degrading imagequality, i.e., the position error of the actuator is within 1% of scansize.

We will now describe one implementation of a controller that operates ata high scan frequency and that minimizes the effects of creep, thermaldrift and the dynamics of a scanner 105 while rejecting position sensornoise. As shown in FIG. 6 controller 100 is configured to employ areference waveform, signal, or dataset “R” (for example, a trianglewave) representative of the desired scanning motion which, duringoperation, is compared to the measured motion of an actuator 110 of ascanner 105 using a comparison block 112. Actuator 110 may be coupled toa probe as shown in FIG. 1, or the sample, or may include a combinationof components that provide motion to either or both. Note that probe 14is often a microfabricated cantilever with an integrated tip. Probealternately can be any of the wide field of probes that are used inscanning probe microscopy (SPM), including, but not limited to, scanningtunneling microscope tips, probes for magnetic force microscopy,electric force microscopy, surface potential microscopy, chemical forcemicroscopy, probes with carbon nanotube or carbon nanofibers, and probesfor aperture-based or apertureless near-field scanning opticalmicroscopy.

Controller 100 in this embodiment employs a relatively slow feedbackloop 104 that compensates for position errors from low frequency sourceslike creep and drift, as well as a feed forward loop 102 thatcompensates for scanner dynamics and/or nonlinearities.

When scanner 105 performs zig-zag raster scanning the turn around motioncorresponds to a large increase in deceleration and acceleration force.Such force, as described previously, contains many high frequencyexcitations which can cause the scanner to resonate uncontrollably. Whensuch resonant motion is superimposed on the linear motion of thescanner, the image will be distorted, showing ripples in the dataadjacent to the turn around corner. And severe resonance can lead to aripple effect throughout the entire image. To reduce the impact of asharp corner at the turn around, the reference waveform R may be lowpass filtered to produce a rounded shape at the peaks, as shown in FIG.3. In one embodiment, the reference waveform R is synthesized by summingtogether the first four Fourier terms of a triangle wave at the scanfrequency f₁. The first four Fourier components including thefundamental f₁ and three overtones at 3f₁, 5f₁, and 7f₁ give a goodapproximation of a linear triangle wave, with the possible exception ofa smoother transition at the peaks. It is possible to use more or fewerFourier components depending on the desired tradeoff between linearityand impulse forces at the turnaround. In one embodiment, a windowtechnique, for example but not limited to a Hanning window, is used toadjust the Fourier components to reduce the amount of ripple caused bythe finite number of Fourier components. The ripple amplitude can bereduced to 1/20^(th) of the ripple amplitude by applying such a window.

The division of labor between the feedback and feed forward loops ispossible because thermal drift and piezo creep typically occur atsubstantially different times than scanner motion and scanner dynamics.Thermal drift and piezo creep have time constants on the scale ofseconds to hours, corresponding to frequencies of about 0.1 Hz to 10⁻⁵Hz. On the other hand, typical conventional AFMs have scanner dynamicsin the range of 10² Hz range with fast AFMs having dynamics in the 10³to 10⁴ Hz or higher. Typical AFM scan speeds range from roughly 0.1 Hzto 10 Hz for conventional AFMs, and up to 10 Hz to 10⁴ Hz for higherspeed AFMs. Thus the low bandwidth feedback loop is generally arrangedto have a bandwidth of less than the scan frequency, but higher than thefrequency associated with drift and creep. As an example, for an SPMsystem scanning at 30 Hz, a feedback bandwidth of 1 Hz is well abovethat required to compensate for drift and creep, but still well belowthe scan frequency.

Prior art feedback loops, as shown for example in FIG. 4, are typicallyarranged to have a controller 58 with a bandwidth well above the maximumscan frequency so that they can faithfully reproduce the referencewaveform 51. This wide bandwidth requirement introduces a largerfraction of the sensor noise into the motion of the scanner. In thecurrent embodiment, however, the low bandwidth of the feedback loopsubstantially attenuates the effect of the sensor noise toscanner/actuator motion.

To illustrate this effect with an example, consider a scanner operatingat a scan frequency f₁ of 10 Hz and subjected to a random sensor noise.To faithfully reproduce a triangle wave reference waveform, the closedloop bandwidth is at least several times the frequency of the referencewaveform. If, as described above, it is desirable to have at least thefirst four Fourier components of the triangle wave well reproduced, thenthe prior art feedback loop would need to have a scan bandwidth of 7f₁,or roughly 70 Hz. If however, the feedback loop is only required tocompensate for creep and/or drift, a bandwidth of 0.1 Hz may be chosen,for example. In a simple case, the sensor noise is a white noise. Socutting the feedback bandwidth from 70 Hz to 0.1 Hz may result inattenuating the impact of sensor noise on actuator position by a factorof

$\sqrt{\frac{70}{0.1}} = 26.$

For a high speed AFM, operating at a scan frequency of say 500 Hz, theimprovement in sensor noise impact could be almost a factor of 200 overthe feedback loop architecture of FIG. 3.

Note that the bandwidth of 7f1 used in this example to estimate thenoise attenuation figure is not required for the present invention.Instead, it is simply used as a convenient benchmark to estimate thereduction in the impact of the sensor noise on the actuator position. Ascan bandwidth can be selected to be larger or smaller than 7f₁depending on the accuracy desired for the scan waveform. Higher scanbandwidths increase the number of Fourier components used to constructthe scan waveform.

Noise in actuator position may be measured in any of several ways. It ispossible, for example, to measure the voltage noise of the controlsignal u (FIG. 6) that drives the actuator, and multiply this by theactuator sensitivity. The total noise in a specified noise bandwidth canbe used to characterize the noise performance of the system. Note thatwe distinguish the term “scan bandwidth” from “noise bandwidth.” Noisebandwidth defines the bandwidth over which a noise measurement isperformed. By specifying a noise bandwidth for noise evaluationpurposes, we are not implying that the system's scan bandwidth be thesame. Also note that the generally triangular waveform would be removedfrom the data prior to a noise analysis. Alternatively, one can measurethe noise in the location of a topographic feature, for example theposition of a step edge on a graphite surface as observed in a SPMimage. A traditional closed loop AFM image may show noise of one toseveral nm on such a step edge, while the current invention can achievenoise of less than 1 Å, on par with the operation of a quality open loopscanner.

Returning to the feedback system, loop 104 employs a closed loopfeedback controller 106 (a PI control block, for instance, implementeddigitally or with analog circuitry), and a sensor 108 which yields asignal 109 representative of detected motion of a scan actuator 110 inresponse to the input signal, u. Note the large noise componentassociated with the detected motion 109. It is this noise thatintroduces noise in the actuator position, illustrated by signal 53 inFIG. 4, using known AFM controllers. However, when using the controllerof this embodiment, the actuator position, as represented by signal 107in FIG. 6, follows the trajectory of desired scanning motion asrepresented by reference R. Overall, contrary to known AFM controllers,noise associated with actuator position (signal 107) compared to thenoise associated with the detected motion (signal 109) is dramaticallyreduced, as shown schematically (exploded) in FIG. 6.

In one embodiment, closed loop feedback controller 106 contains onlyintegral gain for high rejection of sensor noise and low steady stateerror. In this embodiment, the value of the integral gain is set toprovide a control bandwidth sufficiently low to allow substantialrejection of sensor noise, yet sufficiently high bandwidth to compensatefor low frequency creep and/or drift. In this embodiment, the integralgain is set such that the feedback bandwidth is generally lower than thescan frequency. Alternatively, controller 106 may be a PI or PIDcontroller, for example. It may also be a more complex model-basedcontroller that uses prior knowledge about the system properties,nonlinearities and/or hysteretic behavior in addition to feedback.

Based on the position error determined by comparison block 112 feedbackcontroller 106 generates an appropriate control signal, u_(fb).Comparison block 112 may comprise analog circuitry and/or digitalcomputation element(s) that create a signal and/or data representativeof the error between the reference waveform and the measured actuatortrajectory. (Note that the contribution to u from feed forward branch102 (i.e., u_(ff)) will be discussed below.) Controller 106, andspecifically u_(fb), operates to compensate the low frequency positionerror between reference signal “R” defining desired scanner motion andactual scan actuator scanner motion as represented by the output signalof sensor 108. As a result, adverse effects on relative probe-samplepositioning due to creep and/or thermal drift are minimized. Moreover,by operating at low bandwidth, the adverse positioning effects of thesensor noise (high frequency noise) on the control signal, u, and thuson actuator motion, are minimized, as described above. In oneembodiment, the actuators 110 for the x, y and z axes are piezoelectricstacks coupled to flexures with different amounts of stiffness, asdescribed in copending application Ser. No. 11/687,304, filed Mar. 16,2007, entitled “Fast-Scanning SPM Scanner and Method of Operating Same.”However, the actuators can also employ any number of alternativeactuation technologies, including but not limited to, piezoelectrictubes or other piezoelectric devices, actuators formed fromelectrostrictive, magnetorstrictive, electrostatic, inductive, and/orvoice coil drive mechanisms and other actuators that generate motion inresponse to an input signal. Actuator 110 may by itself make up ascanner, for example in the case of a piezoelectric tube. Actuator 110may also be a component of scanner 105 that contains other components,for example, flexure elements that guide and/or amplify the actuatormotion. In practice, the dynamics of both the actuator and the otherscanner components can otherwise limit the maximum scan frequency. Thecurrent invention can be used to generate improved performance of bothindividual actuators and more complex scanner assemblies.

Position sensor 108 most often produces a signal that is indicative ofthe position of actuator 110. Suitable position sensors may also producea signal that is indicative of actuator velocity which may then beintegrated (e.g., by a processor) to determine the relative actuatorposition. Position sensors may be arranged to measure the motion of theactuator directly or the position of a separate reference point orsurface that is moved by the actuator. Position sensor 108 may furtherinclude a preamplifier and/or signal conditioning that amplify,linearize, and/or demodulate the raw signal from the sensor into onethat can be better used by the controller.

We now turn to the operation of the feed forward algorithm. Referringagain to FIG. 6, feed forward branch 102 of controller 100 utilizes afeed forward control algorithm 120 to facilitate high speed scanningwith minimized scanner resonance distortion. In general, a feed forwardalgorithm is an algorithm that uses prior knowledge of the properties ofa system to estimate a control signal required to generate desiredoutput. Feed forward control algorithm 120 is described in furtherdetail below, but primarily uses knowledge of the actuator (or scannerunit) dynamics (i.e., non-linearities, etc.) to generate a feed forwardcomponent, u_(ff), of the scanner control signal u that drives actuator110 along a desired trajectory.

In one embodiment, actuator 110 is exercised with a first estimate of awaveform u_(ff) that will drive the actuator to approximate thereference waveform. This estimate can come from a prior measurement oran initial calibration step, for example. Controller 100 updates thedrive waveform u_(ff) to minimize high frequency errors in scan position(output of comparison block 112) by generating an updated scan controlwaveform u_(ff). In one embodiment, the waveform u_(ff) containselements that suppress oscillation of parasitic resonances of thescanner and/or correct for non-linearities in the actuator. Knownversions of feed forward control algorithms have been describedgenerally in Stemmer, Schitter, Ando, Salapaka, Devasia, and Zou, forexample G. Schitter et al., “A new control strategy for high-speedatomic force microscopy, Nanotechnology 15 (2004) 108-114; Q. Zou etal., “Control Issues in High-speed AFM for Biological Applications:Collagen Imaging Example, Asian J Control 2004 June; 6 (2):164-178; andS. Devasia, et al., “Nonlinear Inversion-Based Output Tracking,” IEEETransactions on Automatic Control, Vol. 41, No. 7 (pp. 930-942) (1996),each of which is expressly incorporated by reference herein.

More particularly, in this case, the feed forward branch 102 ofcontroller 100 operates to reduce, for example, periodic errors,including high frequency position errors, by accounting for the dynamics(e.g., non-linearities) of actuator 110 and/or overall scanner 105during AFM scanning. In one embodiment, feed forward algorithm 120 is anadaptive algorithm, sometimes referred to hereinafter as aninversion-based iterative control (IIC) algorithm, that operates usingsensor error to determine an appropriate control signal u_(ff) forcorrecting position error. The IIC algorithm inverts the transferfunction of the scanner or actuator. Based on the sensor error andprevious control signals, IIC calculates a new control signal u_(ff)that is likely to reduce the measured position errors over the scan. Onesuch IIC algorithm is described by Zou et al. in “Precision tracking ofdriving wave forms for inertial reaction devices”, Review of ScientificInstruments 76 023701 (pp. 203701-1-203701-9), (2005). In oneembodiment, the scan control signal u_(ff) is computed as a scan table,or an array of control values as a function of scan position and/ortime. The scan table associated with the scan actuator is updatedrepeatedly to generate an appropriate u_(ff) to minimize the positionerror as quickly as possible.

With reference to FIG. 7, the operation of feed forward algorithm 120 isdiscussed in further detail. When initiating AFM operation, a usertypically runs a survey scan on the sample. When a region of interest isidentified, the user inputs an offset, scanning size and speed, and aninitial scan table is determined in Block 121 by either previouslystored parameters or a modeled scan table based, for example, on thoseuser inputs and transfer function inversion (described further belowwith respect to FIG. 8). A test scan is then performed using thisinitial scan table (Block 122), and the position error relative to thetarget reference is measured. The algorithm then determines, in Block124, whether the position error relative to the scan size is less thansome percentage, “x.” If so, operation of the feed forward branch 102 ofcontroller 100 is terminated in Block 126 with position errorscompensated using the current scan table to generate an appropriateu_(ff). If not, the controller initiates a new iteration by combiningthe current error and newly adjusted model to generate a new scan tableto further reduce the error. The new scan table is determined with thenext iteration of the feed forward algorithm, “i+1,” in Block 128. Moreparticularly, in Block 122, this new generation scan table is used todrive the scanner (i.e., a correction is determined to update the drive)and a new scanning error is then compared with the error margin “x”again. Optionally, the sensor error may be averaged by performingmultiple cycles of scanning, as noted previously, to substantiallyreduce the noise contribution to the error determination. Continuingiteration(s) will eventually reduce the error below “x” and the finalscan table becomes the drive table for the scanner under current userinput parameters. The feed forward algorithm will iterate until thecurrent scan table yields a position error less than the selected “x”percentage. In practice, the criterion of the final iteration error isusually set as less than about 1% of the full image size, correspondingto a few pixels of data in a 512 pixel scan line.

In one embodiment, the position error used by decision block 124 in FIG.7 is the peak error over the scan waveform. It can optionally be theintegral error over the scan waveform, a subset of the integral error,an RMS error, or any other data or computation that is related to adifference between the commanded position and the position measured by aposition sensor.

In some embodiments, as discussed further below in connection with FIGS.10-12, the ideal threshold of peak error to total scan size is about 1%and a position noise less than about 1 Angstrom RMS within a noisebandwidth equal to about seven times the scan frequency. This result canbe achieved in about 3-4 iterations of the feed forward algorithm, andin some cases may be achieved with initial scan waveform. In practice,this means that position error can be reduced to the 1% threshold inabout 2 seconds. Stable positioning that yields minimal imagedegradation is thereafter maintained at high bandwidth, with the u_(ff)waveform/signal/data array controlling positioning at high bandwidth,and u_(fb) correcting for low bandwidth position errors such as thermaldrift and piezo creep. It is notable that for higher scan speeds, it maytake several iterations (for example, more than 5) to converge to the 1%threshold. In most cases, however, the threshold can be reached in lessthan 5 seconds, and preferably less than two seconds.

Turning to FIG. 8, a block diagram illustrating the components used toproduce an initial scan table 140 processed by feed forward algorithm120 is illustrated. A first component of initial scan table 140 isidentifying one or more transfer functions 142 associated with theactuator 110 and/or scanner as a whole (multiple transfer functions maybe employed for multiple axes and possibly coupling between the axes) tocapture its dynamics). Transfer functions 142 represent the dynamics ofactuator 110. When a drive waveform (e.g., a triangle wave) is appliedto scan actuator 110, typically over a range of frequencies, and themotion of the actuator is measured with a sensor, the scan actuatoryields a particular response, the transfer function. A transfer functionis illustrated graphically in FIGS. 9A and 9B. FIG. 9A shows theamplitude response of the actuator when a constant amplitude drivesignal is swept over a range of frequencies. FIG. 9B illustrates thecorresponding phase response of the scanner. Note that the transferfunction may change based upon operating conditions, and that scannerdynamics represent more than the transfer function(s) (which define thelinear part of the dynamics). Notably, the pre-determined transferfunction is used as part of an overall scheme to optimize the drivewaveform u_(ff).

The transfer functions can be obtained by conventional systemidentification methods. For example, by exciting the scanner with asignal of known frequency and amplitude, the scanner response divided bythe drive signal defines gain and phase at that frequency. By sweepingfrequency throughout the desired range, the transfer function, which isthe gain and phase as a function of frequency for the scanner, can bemeasured. It can also be measured through gain and phase of the responsewhen exciting the scanner with white noise or from system modeling.FIGS. 9A and 9B show an actuator having dynamics at frequenciesapproaching 1 kHz.

The transfer function more specifically represents the expected responseof the actuator to a particular input. In operation, feed forwardalgorithm 120 operates to invert the transfer function, and based on theerror (output of Block 112 in FIG. 6) and previous scan tables,determines an appropriate scan table to provide an appropriate controlsignal, u_(ff) to compensate, in this case, the position error.

With further reference to FIG. 8, the initial scan table is also definedby user selected parameters 144 such as scan size, scan angle andoperating frequency. Notably, using the preferred embodiments, scanfrequencies up to at least one-third the resonant frequency of the scanactuator can be achieved while maintaining position stability. For thescanner illustrated in FIGS. 9A and 9B, this means a scan speed of about300 Hz can be achieved. This is in stark contrast to known AFMs whichtypically scan in the single Hz range. The initial scan table may alsobe defined by a calibrated scanner file 146. Though not necessary tooperate the preferred embodiments, calibrated data associated with thescan actuator may be used in the generation of the initial scan table.These calibrated data is acquired by scanning a sample with an array offeatures having known linear dimensions. Finally, the initial scan tablefor the current measurement may be modified by saved scan tablesassociated with the scan actuator. For instance, scan table informationcorresponding to prior experiments performed by the scan actuator can beemployed to produce an initial scan table that more accurately reflectsactual actuator response in operation, potentially providing acorrespondingly greater chance of achieving the threshold error upon thefirst iteration of the feed forward algorithm. The effect of calibrationis shown in FIG. 12, discussed further below.

The performance of controller 100 is illustrated in FIGS. 10-12. Thevertical axis represents the voltage signal of the corresponding signalswhile the lateral axis is the time in milliseconds. All the signals aresampled simultaneously at different test points in FIG. 6. FIG. 10illustrates a first curve labeled “Reference Signal 1,” which is a puretriangle wave illustrating the desired motion of a scanner, e.g., araster scan. Curve “Drive Signal 2” illustrates the drive signal u_(ff)that is produced by the controller to correct probe-sample positionerrors. Drive signal (i.e., u_(ff)) yields a sensor signal labeled“Sensor Signal” that is substantially coincidental the pure trianglewaveform intended to be produced by the scanner, i.e., Reference Signal.The error between the pure triangle signal or waveform (the ReferenceSignal) and the sensed actuator motion “Sensor Signal” produces an errorprofile represented by “Error Signal.” The “Error Signal” is kept to aminimum through a combination of low bandwidth feedback with highfrequency error compensation using feed forward control algorithm 120 ofcontroller 100. For the case shown in FIG. 10, this amount of error isaccomplished in about 3-4 iterations of feed forward algorithm 120.

FIG. 11 illustrates a blown up version in the vertical axis of theactuator response illustrated in FIG. 10. More particularly, waveforms“Error Signal Before Iteration (ESBI)” and “Error Signal After Iteration(ESAI)” illustrate the error associated with driving the actuator withcontroller 100. More particularly, waveform “ESBI” illustrates theinitial error after the first operation of feed forward algorithm 120.Though relatively large to start, after about 3 to 4 iterations of thefeed forward algorithm, the error is reduced to that shown schematicallyby waveform ESAI. It is this amount of error that is less than thethreshold required for scanning at high speeds without degrading imagequality, i.e., position error is ideally less than 1% of the scan size.Note that ESBI illustrates that the error is typically the greatest atthe transition points of the raster scan, and as such, does notsignificantly impact the resultant image generated by the acquired data.

Turning to FIG. 12, the number of iterations of feed forward algorithm120 to achieve the selected amount of error for fast scanning accordingto one embodiment of the invention is shown. For the case in which thescanner is not calibrated, the number of iterations to achieve, in thiscase, 1% maximum error of the total scan size is about 7 to 8 iterationsof the feed forward algorithm. With the scanner calibrated, however, the1% threshold can be achieved in 3 to 4 iterations as described above. Ineither case, high integrity fast scanning can be performed within about2 seconds of initiating the scan.

In sum, the controller 100 and associated control algorithms of thecurrent invention can improve the scanning speed of a conventional AFMscanner by greater than an order of magnitude. The low bandwidthfeedback controller substantially eliminates the effects of lowfrequency or DC components of the positioning error, while theadaptive-based feed forward control algorithm 120 minimizes the adverseeffects on actuator position associated with high frequency sensordynamics and non-linearity. The two signals produced by each of thecontrol branches, u_(fb) and u_(ff), are combined to provide a controlsignal u which yields substantially linear scanner motion that followsthe reference, such as that shown in FIG. 5, at improved speeds greaterthan 1/100^(th) of the fundamental resonant frequency of the scanner(actuator), and preferably greater than 1/10^(th) the resonant frequencyof the scanner, and more preferably, ⅓^(rd). For a typical piezoelectricactuator usable in the contemplated applications (resonant frequency ofabout 900 Hz), this means scanning at 300 Hz is possible withoutcompromising image quality.

The operation of controller 100 is shown schematically in FIG. 13, aplot of noise density versus scanner frequency. As shown, if the scanbandwidth is set at an appropriate frequency, the feed forwardcontribution, u_(ff), to the scanner control signal, u, can be employedto compensate for high frequency position errors. The feedback controlloop and its contribution, u_(fb), to the scanner control signal, u, isoperated at low bandwidth sufficient to correct low bandwidthcontributions to position error, such as creep and thermal drift. Inthis way, the noise from the position sensor of the feedback loop, andits contribution to noise density, is essentially minimized. Forexample, the scan bandwidth can be set to about seven times the scanfrequency while minimizing the impact of position sensor noise. In sum,by operating feedback loop 104 (FIG. 6) at low bandwidth, the noiseintroduced by the position sensor is minimized to the area 150 shownschematically in FIG. 13. As a result, image integrity is not degradedappreciably while scanning at significantly greater speeds with feedforward algorithm 120 operating to provide a correction for highfrequency position errors.

One practical effect of the more precise positioning provided by thepreferred embodiments is illustrated in FIGS. 14A-14C. FIG. 14Aillustrates a sample of a calibration grating (10 micron pitch size, 100micron scan size, 10 Hz) having a region of interest marked “A” that isto be imaged at high resolution. To move from the probe-sample positionshown in FIG. 14A to the zoomed location “A” while operating theactuator at a high frequency, position errors should be substantiallymaintained, for example, at about 1% of the scan size as achieved by thepreferred embodiments. In that case, region “A” will lie in the zoomedlocation. This is in contrast to known AFMs and their associated controltechnology given that the error at high scan frequencies is large, forexample in the range of, for instance, about 10%. In such a case, movingfrom a 100×100 μm scan range to a 1×1 μm sub-region would yield an errorof about 10 μm, an amount too great to allow the AFM to reliablyposition the probe and sample so that region “A” remains within thecommanded probe-sample position. FIG. 14B illustrates the zoomedlocation “A” (approximately 5 micron area) using the controllerdescribed previously. Turning to FIG. 14C, an image associated with anew scan of the area shown in FIG. 14B (about a 3.2 micron scan at 10Hz) using the present controller illustrates low noise and precisepositioning of the scanner without creep.

Turning to FIGS. 15A-15C, the effect of noise on probe-samplepositioning using known AFMs as well as the present invention isillustrated. Corresponding sample images are of an edge feature imagedusing an AFM having an open loop position controller, FIG. 15A, and aclosed loop position controller, FIG. 15B, with the image of FIG. 15Cshowing an image obtained using an AFM incorporating the presentinvention. More particularly, FIG. 15A illustrates the edge feature withlow noise (amplitude 200) given the lack of a position sensor. FIG. 15Bis an edge image using a conventional closed loop controller whichprocesses sensor noise thereby producing a noisy image. As shown, noise210 is significantly greater than noise 200, as expected. FIG. 15C is animage obtained using the present invention in which the same positioningaccuracy and linearity of a closed loop controller is maintained whileachieving the noise performance of open loop imaging. In other words,actuator noise 220 is reduced significantly compared to the closed loopnoise 210, and is more in the range of the open loop noise 200 shown inFIG. 15A.

Although the best mode contemplated by the inventors of carrying out thepresent invention is disclosed above, practice of the present inventionis not limited thereto. For instance, for very small scan sizes, such astens to hundreds of nanometers, the adaptive procedure of the IICcontrol algorithm can be bypassed completely to avoid divergence ofcalculation. It will be manifest that various additions, modificationsand rearrangements of the features of the present invention may be madewithout deviating from the spirit and scope of the underlying inventiveconcept.

What is claimed is:
 1. A method of operating a metrology instrument,comprising: generating relative motion between a probe and a sample at ascan frequency using an actuator having a fundamental resonancefrequency; detecting motion of the actuator using a position sensor,wherein the position sensor exhibits noise in the detected motion;controlling the XY position of the actuator with a control signal, u,using both a feedback loop and a feed forward algorithm, wherein afeedback signal, u_(fb), associated with the feedback loop is updatedduring operation of the metrology instrument by combining a signalassociated with a predetermined path defined by the feed forwardalgorithm therewith; wherein the the scan frequency is greater than1/100th of the fundamental resonant frequency; and wherein the bandwidthof the feedback loop is different than a bandwidth associated withoperation of the feedforward algorithm.
 2. The method of claim 1,wherein the controlling step includes operating the feedback loop at abandwidth less than the scan frequency associated with the generatingstep thereby attenuating noise in the actuator position compared to thenoise in the detected motion in the corresponding bandwidth, and whereinthe feed forward algorithm substantially continuously updates thecontrol signal so that the XY motion of the actuator substantiallyfollows a reference thereby compensating for the non-linear response. 3.The method of claim 1, wherein the feed forward algorithm includes usingan inversion-based control algorithm.
 4. The method of claim 3, whereinthe inversion-based control algorithm adaptively produces a correctionthat contributes to a control signal that compensates for at least oneof the non-linearities and the dynamics of the actuator.
 5. The methodof claim 4, wherein the control signal produces a peak position error ofless than about 1% of the total scan range after no more than about 10iterations of 10 scan lines per iteration.
 6. The method of claim 5,wherein the control signal produces a peak position error of less thanabout 1% of the total scan range after no more than about 5 seconds. 7.The method of claim 1, wherein the fundamental resonant frequency of theactuator is greater than about 100 Hz and the scan frequency is at leastabout 100 Hz.
 8. The method of claim 7, wherein the scan frequency is atleast about 300 Hz.
 9. The method of claim 1, wherein the bandwidth ofthe feedback loop is less than the scan frequency.
 10. The method ofclaim 1, wherein the bandwidth of the feedback loop is less than about10 hz.
 11. The method of claim 1, wherein the controlling stepattenuates the noise in the actuator position to less than about 1Angstrom RMS within a noise bandwidth equal to about seven times thescan frequency.
 12. The method of claim 11, wherein the controlling stepincludes using a PI controller.
 13. A method of operating a metrologyinstrument, comprising: generating, with an actuator exhibiting anon-linear response, relative motion between a probe and a sample at ascan frequency over a scan size; detecting motion of the actuator usinga position sensor; calibrating the actuator to generate an initial scantable; controlling the XY position of the actuator with a controlsignal, u, using both a feedback loop and a feed forward algorithm,wherein a feedback signal, u_(fb), associated with the feedback loop isupdated during operation of the metrology instrument by combining asignal, u_(ff), associated with a predetermined path defined by the teedforward algorithm therewith, wherein the scan table is updatedrepeatedly during operation to generate u_(ff) thereby causing the feedforward algorithm to substantially continuously update the controlsignal so that the XY motion of the actuator substantially follows areference thereby compensating for the non-linear response; and whereinthe bandwidth of the feedback loop is less than about 10 Hz, and thebandwidth of the feedforward algorithm is greater than about 300 Hz, andthe scan frequency is greater than 100 Hz.
 14. The method of claim 13,wherein the feed forward algorithm is an adaptive feed forward algorithmthat estimates a transfer faction of the actuator in response to theposition error and adjusts the generating step based at least in part onthe transfer function.
 15. The method of claim 14, wherein the responseof the actuator is dependent on an operating condition, wherein theoperation condition is at least one of scan frequency, size, angle, andoffset.
 16. The method of claim 13, wherein the scan frequency isgreater than about 300 Hz.
 17. A scanning probe microscope (SPM)comprising: an actuator exhibiting a non-linear response that generatesrelative motion between a probe and a sample at a scan frequency; asensor that detects motion of the actuator and generates noise; acontroller including a feedback loop that generates an XY positioncontrol signal, u, based on the detected motion; wherein the actuator iscalibrated to generate an initial scan table; wherein a feedback signal,u_(fb), associated with the feedback loop is updated during operation ofthe metrology instrument by combining a signal, u_(ff), associated withthe scan table, wherein the scan table is updated repeatedly duringoperation to generate u_(ff) thereby causing the feed forward algorithmto substantially continuously update the control signal; wherein thebandwidth of the feedback loop is less than the scan frequency therebyattenuating noise in the actuator position compared to the noise in thedetected motion; and wherein the bandwidth of the feedback loop isdifferent than a bandwidth associated with operation of the feedforwardalgorithm.
 18. The SPM of claim 17, wherein the XY motion of theactuator substantially follows a reference thereby compensating for thenon-linear response.